Most pets that are disabled want to be mobile again. However, some pets will not readily use a cart in the beginning. There can be a couple of reasons for this.
Some pets are simply not strong enough in the front quarters to use a cart. You can test their front end strength by sling walking them around the yard. If your pet tires quickly, then he or she may not be strong enough to use a cart. This is especially important in older pets. They often have arthritic or neurological changes in the front end that will make them weak.

Some pets may be timid, making them fearful of the cart. These pets can be desensitized by leaving the cart in plain sight where they spend the majority of their time. Bed, food bowl, etc.
For these pets, I like to go very slowly. Don’t ask too much too fast. Let them get used to the idea before asking them to actually use it. Try it on, take it off. Praise, repeat. When walking these pets for the first few times, we recommend using a leash to help steady them and keep their speed controlled. There are no rules for how long it may take. Lots of praise and goodies can make this a pleasant experience for the timid ones.

One Happy Dachshund!